In practice, much larger capacitance values, even 2-3 times the originals, work fine for filters, although larger capacitors have higher series resistance, which can make the filtering worse or cause the capacitors to run hotter and wear out sooner. However, on most circuit boards there isn't enough room for bigger capacitors than the originals, so check the dimensions of any replacements. For switching power supplies (any regulator on a motherboard, most of a monitor's high voltage circuitry, the low voltage part of any PC supply), make sure they're rated for 105 Celcius and for high frequency operation or they may wear out in less than a year. Also look at the lifespan rating, which ranges from about 1,000-7,000 hours @ 105C. Digi-key and
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Filter capacitors are used ahead of the voltage regulators to maintain minimum DC voltage because the voltage comes in as AC (sometimes converted from DC) that's fed through diodes to convert it to pulsating DC, and the capacitors then turn this into more steady DC.
Filter capacitors are also needed to prevent excessively large voltage spikes because chips draw large amounts of power in brief bursts each time they toggle signals high and low. Without adequate filtering, these spikes can cause erratic operation and even damage the chips.